Non‐linear nonparametric quality screening in low sampling testing

Purpose – Screening simultaneously for effects and their curvature may be useful in industrial environments when an economic restriction on experimentation is imposed. Saturated‐unreplicated fractional factorial designs have been a regular outlet for scheduling screening investigations under such circumstances. The purpose of this paper is to devise a practical test that may simultaneously quantify in statistical terms the possible existence of active factors in concert with an associated non‐linearity during screening. Design/methodology/approach – The three‐level, nine‐run orthogonal design is utilized to compute a family of parameter‐free reference cumulative distributions by permuting ranked observations via a brute‐force method. The proposed technique is simple, practical and non‐graphical. It is based on Kruskal‐Wallis test and involves a sum of effects through the squared rank‐sum inference statistic. This statistic is appropriately extended for fractional factorial composite contrasting while avoiding explicitly the effect sparsity assumption. Findings – The method is shown to be worthy competing with mainstream comparison methods and aids in averting potential complications arising from the indiscriminant use of analysis of variance in very low sampling schemes where subjective variance pooling is otherwise enforced. Research limitations/implications – The true distributions obtained in this paper are suitable for sieving a fairly small amount of potential control factors while maintaining the non‐linearity question in the search. Practical implications – The method is objective and is further elucidated by reworking two recent case studies which account for a total of five saturated screenings. Originality/value – The statistical tables produced are easy to use and uphold the need for estimating separately mean and variance effects which are rather difficult to pinpoint for the fast track, low‐volume trials this paper is intended to.